Original ledger status
DIAMOND.PARA.SELFCODE.01
THE PARABOLIC ANCHOR SELF-CODE (2026-07-31; external structural review audited by discovery probe parabolic_selfcode_audit_probe.py 23/23, verdict SELFCODE-VERIFIED, and promoted; one module, 14 checks, ~1 s, exact integer/symbolic sympy, no floats). The v218 sheet-diamond direction operators U = Q diag(1,0,0) (rank-1 winding) and V = Q diag(0,1,1) (rank-2 sheet, Spec V = {0,1,2}) carry a previously unstated exact operator structure. (1) PARABOLIC THEOREM: A = Q<I,U,V> is the FULL line-stabiliser (maximal parabolic) algebra of block type 2|1 -- seven words independent (coordinate det -81), multiplicatively closed (49/49), all seven matrix units contained, dim 7 = 9-2; mutation of Q's third column breaks it. (2) DOUBLE SELF-CODE: Pi2 = V(V-I)/2 idempotent trace-1; H = I + Pi2 has spectrum EXACTLY {1,1,2} = a (ANCHOR.GEN.01/v23); chi_H = x^3 - 4x^2 + 5x - 2 with (e1,e2,e3) = (4,5,2) = (|mu4|, g_car, |Z2|) AND = (dim_R(GL3/P), dim(A/J), dim J) -- the anchor reproduced spectrally (dominant projector of V) and categorically (flag/Levi/radical of A) from ONE structure. (3) UNIQUENESS THEOREM: x^3 - 2m x^2 + (m^2+1) x - m = (x-m)(x^2-mx+1) identically; positive-integer spectra force m^2 - 4 = k^2, (m-k)(m+k) = 4, m = 2 UNIQUELY -- a = (1,1,2) is the only anchor this parabolic family can code. (4) THE 81 AS LATTICE INDEX: the SATURATED integral order (closure stable at word length 4) has elementary divisors (1,1,1,3,3,3,3): [P_Z : Z<U,V>] = 3^4 = 81, cokernel (Z/3)^4 -- equal to the v218 determinant-staircase sum 3+4+8+14+20+32 = N_fam^4 (cross-link typed; the mark-local mechanism, one Z/3 per mu4 mark, stays [O]: if no canonical local decomposition exists the 81 stays a fingerprint). (5) A2 BIT CARRIER: the basic algebra e A e is the A2 path algebra (dim Ext^1 = 1): dim-vector-(1,1) modules fall into EXACTLY two iso classes (split / one nonsplit) -- the alignment bit gains a canonical algebra carrier; uniqueness [E], SELECTION stays with RP/geometry (v528/v534) [C]. (6) TRACE CODE (re-encoding): p_n(a) = 2 + 2^n = 1 + tr(V^n); recurrence, Hankel 2^{n+1}; (1+trV)(1+trV^2)(1+trV^3) = 240 = |R(E8)|; tr(V^4-V^3) = 8 = rank E8 -- AnchorLadder read through V, one object fewer, NO new content. (7) CR TEST DESIGN (CONTRACT.F.01): CR(alpha_{-2},alpha_{-1};alpha_0,alpha_1) = 4/3 exactly on the v533 line; honesty wired (universal arithmetic-progression cross-ratio -- content = preregistered solver-state export); negative control 28/25; y_F forced fit-free. (8) LORENTZ FORM (reformulation): det X = t^2 - x^2 - y^2 under Phi; D(P,Q) = 2<Phi,Phi>_{1,2}; delta = sech^2(atanh r); pencil identities det(B-S) = det B det(I-Z), D(B,S) = det B tr Z, det S = det B det Z -- eigenvalue locking as the named prime-front instrument (no measurement, no RH statement). NAMED LIMITS AS CONTENT: NO P2 REDUCTION -- 'g_car = dim(A/J) derived' is conditional on the OPEN 'No Carrier Reconstruction' audit (rebuild Q/V from mu4, D4, Q_+ = A3 exponent grading, H^1, Q_- = sheet monodromy, WITHOUT g_car, a, rank E8 or carrier-aware budgets; Q's historical provenance runs through such budgets); AX.P2.01 and ANCHOR.GEN.01 markers UNTOUCHED; the 2..9 dimension table is COMPRESSION of one operator system, not nine independent hits (no-free-pattern rule); the bit selection, the mark-local 81 mechanism and the CR-test execution stay open and typed open; the word 'derived' appears nowhere for any physics statement. UPDATE (2026-07-31, v567): the review's Priority-1 audit is EXECUTED at Stage A -- verdict RECONSTRUCTS-TO-FAMILY: the anchor self-code is carrier-free; Q reconstructs up to one binary sheet-coupling choice; see QGEO.QRECON.01. FURTHER UPDATE (2026-07-31, v568): Priority 3 executed -- the A2 Ext arrow is NONZERO on the whole reconstruction class (the split member collapses to dim 5 and is excluded); Priority 2 sharpened -- the mu4-grading candidate fails, the F3[V]-action on the cokernel exists (see DIAMOND.BIT.SELECT.01). [2026-07-31: the S8 pencil identities are now executed on the REAL Paper-II surface by v569 (machine-tight at 2e-14 on 70 windows, verdict ONE-MODE); see PRIME.PENCIL.ONEMODE.01.] [2026-08-01 X: the per-mark Z/3 mechanism appears geometrically -- v597: the cusp-class group of the mu3-cover is (Z/3)^4 of order 81 with four free local classes; see QGEO.COVER.01.] [2026-08-01 XVI: the self-code algebra has a geometric realization -- v600: (U, V) as Gamma-even degree-2 cusp-Gram operators on the mu3-cover, GL3-conjugate to the compiler pair, with the SAME saturated Z-order structure (index 81 = 3^4, divisors (1,1,1,3,3,3,3)); existence [E], canonicity open; see QGEO.EMBED.01.]
Recorded status: Identity [E] (exact integer/symbolic algebra with mutation controls -- parabolic closure, double self-code, uniqueness enumeration + divisor argument, saturated Smith form, A2 quiver, trace code, cross-ratio identities, Lorentz/pencil identities) + [C] (the TFPT readings of the invariants; the bit-carrier and CR-test interpretations) + [O] (the No-Carrier-Reconstruction audit, the mark-local 81 mechanism, the CR-test execution); NO marker moves
Dependencies, status detail and source
Canonical status: [E] A = full 2|1 parabolic, dim 7, word det -81, closed 49/49, mutation-fragile; a = Spec(I + V(V-I)/2) = (1,1,2) with chi_H = x^3 - flag x^2 + Levi x - radical (4,5,2 double-coded); m = 2 unique (enumeration to 2000 + divisor argument); saturated Smith (1,1,1,3,3,3,3), index 81 = 3^4 = staircase sum; A2 Ext^1 = 1 (two module classes); p_n = 1 + tr V^n (240, rank 8 as traces); CR = 4/3 design with 28/25 control; Lorentz/pencil identities exact; 14/14 checks
Dependencies: DIAMOND.AXIS.01; ANCHOR.GEN.01; AX.P2.01; FLAV.QGEO.01; CONTRACT.F.01; SEAM.BIT.RPBLIND.01; FORM.LADDER.01; v23; v218; v224; v528; v533; v534
Scripts: v566_parabolic_anchor_selfcode.py
Location: tfpt_1;tfpt_2;tfpt_research_contracts
Original CSV, line 605Original ledger status
QGEO.QRECON.01
THE NO-CARRIER-RECONSTRUCTION AUDIT, STAGE A (2026-07-31; Priority 1 of the self-code review; one module, 9 checks, ~1 s, exact enumeration with integer prefilters + sympy verification; discovery probe carrier_free_q_reconstruction_probe.py 10/10, verdict RECONSTRUCTS-TO-FAMILY). THE QUESTION: can Q -- hence V and the v566 parabolic anchor self-code -- be reconstructed WITHOUT carrier/anchor inputs? THE CIRCULARITY LOCATED: v11's uniqueness certificate for Q enumerates over row sums (4,5,6), column sums (9,5,1) and chi_Q = (t-1)(t^2-5t+3) -- the 5 = g_car sits in the budgets and in chi_Q; all of it FORBIDDEN here. ALLOWED (each carrier-free, with corpus source): (S) Sigma = diag(1,-1,-1) [v10 sheet]; (W) Q(I+Sigma) = 2 N_fam W [v10 winding]; (E) Spec(Q_+) = {1,2,3} [FLAV.QGEO.01, A3 exponents]; (M) Q_- != 0, Q_-^2 = N_fam P, P^2 = P [FLAV.QGEO.01]; (Z) nonneg integers, bound 6 (robust at 9); (L) the seam-line demand [geometric, [C]]; (X) the saturation index N_fam^4 = 81 [v566 S4]. RESULTS [E]: (1) exactly 52 admissible matrices under (S)(W)(E)(M)(Z), corpus Q among them, first column forced to N_fam(1,1,1) by (W); (2) the seam-line demand cuts 52 -> 28 (real teeth); (3) THE ANCHOR IS CARRIER-FREE: all 28 parabolic members code the SAME anchor -- H' = I + Pi_dom(V') with char poly x^3 - 4x^2 + 5x - 2, spectrum (1,1,2) = a, ONE code class, no exceptions: the anchor self-code sits UPSTREAM of the carrier budgets, conditional on the declared geometric inputs; (4) THE RESIDUAL BIT: the 81-pin selects EXACTLY TWO members -- the corpus Q (q32 = 2 = |Z2|) and Q_alt (q32 = 0), difference matrix 2 E32 (the sheet-block coupling); every classical carrier-free certificate coincides on the pair (anticommutator spectrum {6,-4,-2} = (|R+(A3)|, -|mu4|, -|Z2|); commutator charpoly t(t^2+12); det = 3; saturation 81), while the ONE separating certificate is the carrier column budget (9,5,1) vs (9,3,1) -- exactly the forbidden input: the residual freedom is ONE binary coupled-vs-uncoupled sheet-block choice; (5) ablations: dropping (W) widens the bound-3 set 28 -> 1376 over 36 first columns (the winding input carries real load); bound robustness 6 -> 9 adds zero new (L)+(X) members; the forbidden inputs were evaluated nowhere. NAMED LIMITS AS LOAD-BEARING CONTENT: STAGE A ONLY -- whether (S)(W)(E)(M)(L) themselves derive from mu4/D4/H^1 parabolic geometry without family/sheet inputs is EXACTLY the open gate GATE.QGEO.01: the audit is RELOCATED there, not closed (N_fam = 3 is used throughout; family data was never forbidden -- the forbidden list is the CARRIER list); the carrier-free selector of the residual bit is OPEN, and its structural resonance with the split/nonsplit alignment-bit dichotomy (v528/v534, v566 S5) is a TYPED OBSERVATION, not a claim; NO P2 reduction -- AX.P2.01 and ANCHOR.GEN.01 markers untouched; the word 'derived' appears nowhere for any physics statement. UPDATE (2026-07-31, v568, DIAMOND.BIT.SELECT.01): the residual bit is located and given a canonical witness -- the twins generate different integral orders, and the ladder self-consistency (dominant mode = its own eigenvalue ladder (1,2,4)) selects the compiler Q uniquely on all 28 members; the split geometry (q32 = 1) is excluded by the demands already imposed; the physical selection stays open. Markers unchanged. [2026-07-31: Stage B narrowed by v574 -- the involution type is forced by a rank theorem and N_fam = 3 by the double self-consistency (ladder + sat = N^4); (E)(M)(L) stay the remaining gate; see QGEO.WINDING.SELF.01.]
Recorded status: Identity/enumeration [E] (exact admissible-set census 52/28/2 with integer prefilters verified by sympy on survivors; one anchor code class on all 28; separator dissection exact; ablations quantified) + [C] (the seam-line demand as declared geometric input; the bit-resonance observation) + [O] (Stage B = GATE.QGEO.01 relocation; the binary selector); verdict RECONSTRUCTS-TO-FAMILY; no marker moves
Dependencies, status detail and source
Canonical status: [E] 52 admissible under (S)(W)(E)(M)(Z) at B = 6; 28 under the seam-line demand; ONE anchor code x^3-4x^2+5x-2 = spectrum (1,1,2) on all 28 (carrier-free anchor); 81-pin -> exactly 2 (corpus Q vs q32 = 0 twin; all carrier-free certificates equal, separator = the forbidden column budget (9,5,1)); winding ablation 28 -> 1376 at bound 3; bound-stable at 9; 9/9 checks; verdict RECONSTRUCTS-TO-FAMILY
Dependencies: DIAMOND.PARA.SELFCODE.01; FLAV.QGEO.01; GATE.QGEO.01; FLAV.KQ.01; AX.P2.01; ANCHOR.GEN.01; v10; v11; v218; v566
Scripts: v567_carrier_free_q_reconstruction.py
Location: tfpt_1;tfpt_2
Original CSV, line 606Original ledger status
DIAMOND.BIT.SELECT.01
THE RESIDUAL RECONSTRUCTION BIT: LOCATED, SEPARATED, AND GIVEN A CANONICAL EXACT WITNESS (2026-07-31; Priorities 2+3 of the self-code review fused with the v567 residual bit; one module, 11 checks, ~1 s; discovery probe bit_selector_probe.py 10/10, verdict SELECTOR-FOUND). (1) THE BIT IS INTEGRALLY VISIBLE [E]: the two 81-twins of the v567 audit (q32 = 2 = |Z2| vs q32 = 0) generate DIFFERENT integral orders -- Hermite bases differ at EQUAL index 81 and equal Smith divisors (1,1,1,3,3,3,3): real integral structure where every classical carrier-free invariant coincides. (2) THE SELECTOR [E]: the dominant mode of the sheet direction satisfies V_c (1,2,2c)^T = 2 (1,2,2c)^T identically in the coupling c; the LADDER SELF-CONSISTENCY -- the dominant mode reproduces its own eigenvalue as the geometric ladder (2^0,2^1,2^2) = (1,2,4) -- forces c = 2: on ALL 28 members of the v567 parabolic carrier-free class EXACTLY ONE satisfies it, the compiler Q, with no 81-pin and no column budget. (3) THE WITNESS IS PRIOR STRUCTURE [C] (no-free-pattern): (1,2,4) is the binary AnchorLadder step sequence p_{n+1} - p_n = 2^n (Lean-formalised), 2 = |Z2| the sheet datum, and the v566 trace code p_n(a) = 1 + tr(V^n) = 2 + 2^n rides the same ladder (n = 1..6 re-verified exactly). (4) THE SPLIT GEOMETRY LOCATED AND EXCLUDED [E]: an invariant module complement of the seam line exists IFF q32 = 1 (exact solve: a = 0, b = 1, q32 = 1; the plane span((1,0,0),(0,1,1)) exactly invariant there), and that member's direction algebra COLLAPSES to dimension 5 (Smith (1,1,1,3,3), no full parabolic, no 81): the seam-line + saturation demands admit ONLY nonsplit geometry -- the v566 A2 Ext arrow is NONZERO on the whole reconstruction class; neither twin splits (the complement system is inconsistent for q32 in {0,2}): the bit does NOT toggle split/nonsplit -- it toggles WHICH nonsplit integral order is realised and whether the dominant mode carries the full binary ladder. (5) PRIORITY-2 CANDIDATE TESTS [E], honest both ways: the mu4-grading candidate deg(E_jk) = g_k - g_j mod 4 FAILS (the order is not a graded sublattice: 5 of 7 Hermite vectors homogeneous) -- the review's kill condition does NOT fire and the 81 stays a FINGERPRINT pending a mechanism; left multiplication by V PRESERVES the order lattice and induces a canonical F3-linear action on the cokernel (Z/3)^4 -- the F3[V]-character computation is EXECUTED: the induced action has characteristic polynomial x(x-1)^2(x+1) mod 3 -- eigenvalues {0,1,1,-1}, NOT the regular mu4 pattern x^4 - 1 that 'one Z/3 per mark' would require (not even invertible), U acts as ZERO, and both twins give the identical structure: after two candidates (grading, V-action) the 81 stays a FINGERPRINT; the kill condition (no canonical local decomposition at all) is closer but not proven. NAMED LIMITS AS LOAD-BEARING CONTENT: the PHYSICAL selection is NOT derived -- why the dominant mode should satisfy the ladder self-consistency is the relocated open question, the same structural slot as the RP-selection of the alignment bit (v528/v534); the resonance between the reconstruction bit and the alignment bit is a TYPED OBSERVATION, not an identification; Stage B of v567 (GATE.QGEO.01) untouched; NO P2 reduction; AX.P2.01 and ANCHOR.GEN.01 markers untouched; the word 'derived' appears nowhere for any physics statement. [2026-07-31: the RP form is spectrally blind but integrally ANCHOR-VISIBLE on the twins (v572, Smith slot 18 vs 2 = 9 = N_fam^2); the dynamical RP-slot stays open; see DIAMOND.BIT.RPFORM.01.] [2026-07-31 II: the review's Ext-sensitive marked resolvent chi_Ext(z) = tr(P_seam R N_Ext R) vanishes IDENTICALLY for both twins with the natural markings (P_seam = E33, N_Ext = the radical lattice generators -- which are IDENTICAL between the twins: span{3E31, 3E32}); the review's own kill criteria fire -- the Gibbs pencil (v572) remains the one working marked object; sandbox record, no module.]
Recorded status: Identity [E] (exact integer/symbolic algebra -- Hermite/Smith lattice comparison, the symbolic dominant-mode identity, the uniqueness census on the 28-member class, the split-complement solve, the candidate tests) + [C] (the anchored ladder selector as candidate canonical selection; its physical justification open) + [O] (the selection mechanism; the F3[V]-character question; Stage B); verdict SELECTOR-FOUND; no marker moves
Dependencies, status detail and source
Canonical status: [E] twins integrally distinct (H0 != H2 at equal index 81); v(c) = (1,2,2c) identically; ladder self-consistency <=> c = 2, unique on 28/28; witness = AnchorLadder 2^n / |Z2| / trace code; split member q32 = 1 (complement solve a=0,b=1) collapses to dim 5 -- excluded; mu4-grading candidate fails (5/7 homogeneous); F3[V]-action computed: charpoly x(x-1)^2(x+1) mod 3, eigenvalues {0,1,1,-1} != regular mu4, U-action zero, twins identical; 11/11 checks; verdict SELECTOR-FOUND
Dependencies: QGEO.QRECON.01; DIAMOND.PARA.SELFCODE.01; DIAMOND.AXIS.01; SEAM.BIT.RPBLIND.01; FORM.LADDER.01; v10; v218; v528; v534; v566; v567
Scripts: v568_bit_selector_ladder.py
Location: tfpt_1;tfpt_2
Original CSV, line 607